Full description
The Semigroups package is a GAP package for semigroups, and
monoids. There are particularly efficient methods for finitely
presented semigroups and monoids, and for semigroups and monoids
consisting of transformations, partial permutations, bipartitions,
partitioned binary relations, subsemigroups of regular Rees 0-matrix
semigroups, and matrices of various semirings including boolean
matrices, matrices over finite fields, and certain tropical
matrices. Semigroups contains efficient methods for creating
semigroups, monoids, and inverse semigroups and monoids, calculating
their Green's structure, ideals, size, elements, group of units,
small generating sets, testing membership, finding the inverses of a
regular element, factorizing elements over the generators, and so
on. It is possible to test if a semigroup satisfies a particular
property, such as if it is regular, simple, inverse, completely
regular, and a large number of further properties. There are methods
for finding presentations for a semigroup, the congruences of a
semigroup, the maximal subsemigroups of a finite semigroup, smaller
degree partial permutation representations, and the character tables
of inverse semigroups. There are functions for producing pictures of
the Green's structure of a semigroup, and for drawing graphical
representations of certain types of elements.
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